How do you solve the following system: $3x - 4y = -10, 4x + 7y = 6x$ ?

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Answer 1 · 2016-02-08T09:52:55

$x=-70/13" "$ I have left the derivation of y for the reader to determine.

Given:

$3x-4y=-10" "$ .................................(1)
$4x+7y=6x" "$ ......................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation (2)

Subtract $4x$ from both sides

$7y=2x$

Divide both sides by 7

$y=2/7x" "......................................(2_a)$

Substitute $(2_a)" into "(1)$

$3x-4(2/7x)=-10" "...................(1_a)$

$3x-8/7x=-10$

$x(21-8)/7=-10$

$x=-(7/13xx10)$

$x=-70/13" ".......................................(1_b)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You can now find $y$ by substituting $(1_b)$ into either of (1) or (2).

I will leave that for the reader to do

How do you solve the following system: 3x - 4y = -10, 4x + 7y = 6x3x - 4y = -10, 4x + 7y = 6x?